Journal ArticleDOI
Nonlinear partial differential equations on homogeneous spaces
TLDR
In this paper, the work of A.K.N.S. which is based on the sl(2, R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations.Abstract:
The work of A.K.N.S. which is based on the sl(2, R) valued soliton connection is extended to obtain new integrable coupled nonlinear partial differential equations. This is achieved by assuming the soliton connection having values in a simple Lie, Kac-Moody, Lie superalgebras. Extensions of some of the integrable nonlinear partial differential equations are given explicitly. In particular the coupled NLS equations on various homogeneous spaces and the coupled modified KdV integro-differential equations are obtained on symmetric spaces.read more
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Journal ArticleDOI
An approach to generate superextensions of integrable systems
TL;DR: In this paper, the trace identity due to Tu is extended to the super case and used to establish Hamiltonian structures of superextensions of integrable systems under consideration, and some new examples of SUPERE EXTensions of Integrable Systems are illustrated.
Journal ArticleDOI
Nonlocal Fordy-Kulish equations on symmetric spaces
TL;DR: In this article, the authors presented nonlocal integrable reductions of the Fordy-Kulish system of nonlinear Schrodinger equations on Hermitian symmetric spaces.
Book ChapterDOI
Integrable Nonlocal Reductions
Metin Gürses,Aslı Pekcan +1 more
TL;DR: In this paper, the Ablowitz-Musslimani nonlocal reduction of nonlinear Schrodinger (NLS) and modified Korteweg-de Vries (mKdV) systems is used to obtain soliton solutions of these nonlocal equations by using the Hirota method.
Journal ArticleDOI
Nonlinear Schrödinger equations and N = 1 superconformal algebra
H.T. Özer,S. Salihoğlu +1 more
TL;DR: By using AKNS scheme and soliton connection taking values in N ǫ = 1 superconformal algebra, they obtained new coupled super nonlinear Schrodinger equations as discussed by the authors.
Journal ArticleDOI
The finite-dimensional super integrable system of a super NLS-mKdV equation
TL;DR: In this article, the super Hamiltonian structure of a NLS-mKdV hierarchy is obtained by making use of super-trace identity, and an explicit super Bargmann symmetry constraint and its associated binary nonlinearization of Lax pairs are carried out for the super NLSmkdV system.